Metamath Proof Explorer


Theorem biimp3a

Description: Infer implication from a logical equivalence. Similar to biimpa . (Contributed by NM, 4-Sep-2005)

Ref Expression
Hypothesis biimp3a.1 ( ( 𝜑𝜓 ) → ( 𝜒𝜃 ) )
Assertion biimp3a ( ( 𝜑𝜓𝜒 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 biimp3a.1 ( ( 𝜑𝜓 ) → ( 𝜒𝜃 ) )
2 1 biimpa ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )
3 2 3impa ( ( 𝜑𝜓𝜒 ) → 𝜃 )